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Rank-optimal weighting or "How to be best in the OECD Better Life Index?"

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  • Jan Lorenz
  • Christoph Brauer
  • Dirk A. Lorenz

Abstract

We present a method of rank-optimal weighting which can be used to explore the best possible position of a subject in a ranking based on a composite indicator by means of a mathematical optimization problem. As an example, we explore the dataset of the OECD Better Life Index and compute for each country a weight vector which brings it as far up in the ranking as possible with the greatest advance of the immediate rivals. The method is able to answer the question "What is the best possible rank a country can achieve with a given set of weighted indicators?" Typically, weights in composite indicators are justified normatively and not empirically. Our approach helps to give bounds on what is achievable by such normative judgments from a purely output-oriented and strongly competitive perspective. The method can serve as a basis for exact bounds in sensitivity analysis focused on ranking positions. In the OECD Better Life Index data we find that 19 out the 36 countries in the OECD Better Life Index 2014 can be brought to the top of the ranking by specific weights. We give a table of weights for each country which brings it to its highest possible position. Many countries achieve their best rank by focusing on their strong dimensions and setting the weights of many others to zero. Although setting dimensions to zero is possible in the OECD's online tool, this contradicts the idea of better life being multidimensional in essence. We discuss modifications of the optimization problem which could take this into account, e.g. by allowing only a minimal weight of one. Methods to find rank-optimal weights can be useful for various multidimensional datasets like the ones used to rank universities or employers.

Suggested Citation

  • Jan Lorenz & Christoph Brauer & Dirk A. Lorenz, 2016. "Rank-optimal weighting or "How to be best in the OECD Better Life Index?"," Papers 1608.04556, arXiv.org.
  • Handle: RePEc:arx:papers:1608.04556
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    Cited by:

    1. Jesús Peiró-Palomino & Andrés J. Picazo-Tadeo, 2018. "Assessing well-being in European regions. Does government quality matter?," Working Papers 2018/06, Economics Department, Universitat Jaume I, Castellón (Spain).
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    3. Jesús Peiró-Palomino & Andrés J. Picazo-Tadeo, 2018. "OECD: One or Many? Ranking Countries with a Composite Well-Being Indicator," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 139(3), pages 847-869, October.
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    5. Peiró-Palomino, Jesús & Picazo-Tadeo, Andrés J. & Tortosa-Ausina, Emili, 2021. "Measuring well-being in Colombian departments. The role of geography and demography," Socio-Economic Planning Sciences, Elsevier, vol. 78(C).
    6. Jose Manuel Cordero & Cristina Polo & Javier Salinas-Jiménez, 2021. "Subjective Well-Being and Heterogeneous Contexts: A Cross-National Study Using Semi-Nonparametric Frontier Methods," Journal of Happiness Studies, Springer, vol. 22(2), pages 867-886, February.
    7. Jesús Peiró-Palomino & Andrés J. Picazo-Tadeo & Emili Tortosa-Ausina, 2020. "The Geography of Well-being in Colombia," Working Papers 2020/03, Economics Department, Universitat Jaume I, Castellón (Spain).
    8. Jesús Peiró‐Palomino & Andrés J. Picazo‐Tadeo & Vicente Rios, 2020. "Well‐being in European regions: Does government quality matter?," Papers in Regional Science, Wiley Blackwell, vol. 99(3), pages 555-582, June.
    9. Luis César Herrero-Prieto & Iván Boal-San Miguel & Mafalda Gómez-Vega, 2019. "Deep-Rooted Culture and Economic Development: Taking the Seven Deadly Sins to Build a Well-Being Composite Indicator," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 144(2), pages 601-624, July.
    10. Shunichi Hienuki & Kazuhiko Noguchi & Tadahiro Shibutani & Takahiro Saigo & Atsumi Miyake, 2019. "The Balance of Individual and Infrastructure Values in Decisions Regarding Advanced Science and Technology," Sustainability, MDPI, vol. 11(12), pages 1-15, June.
    11. Greco, Salvatore & Ishizaka, Alessio & Resce, Giuliano & Torrisi, Gianpiero, 2017. "Is the Grass Always Greener on the Other Side of the fence? Composite Index of Well-Being Taking into Account the Local Relative Appreciations in Better Life Index," MPRA Paper 82718, University Library of Munich, Germany.
    12. Tahsin Mehdi, 2019. "Stochastic Dominance Approach to OECD’s Better Life Index," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 143(3), pages 917-954, June.
    13. Koronakos, Gregory & Smirlis, Yiannis & Sotiros, Dimitris & Despotis, Dimitris K., 2020. "Assessment of OECD Better Life Index by incorporating public opinion," Socio-Economic Planning Sciences, Elsevier, vol. 70(C).
    14. Jesús Peiró-Palomino, 2019. "Regional well-being in the OECD," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 17(2), pages 195-218, June.
    15. Jesús Peiró-Palomino & Andrés J. Picazo-Tadeo & Vicente Rios, 2020. "Social Progress Around the World: Measurement, Evolution and Convergence," Working Papers 2006, Department of Applied Economics II, Universidad de Valencia.
    16. Resce, Giuliano & Maynard, Diana, 2018. "What matters most to people around the world? Retrieving Better Life Index priorities on Twitter," Technological Forecasting and Social Change, Elsevier, vol. 137(C), pages 61-75.
    17. Thananon Buathong & Anna Dimitrova & Paolo Miguel M. Vicerra & Montakarn Chimmamee, 2021. "Years of Good Life: An illustration of a new well-being indicator using data for Thailand," Vienna Yearbook of Population Research, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna, vol. 19(1), pages 547-583.
    18. Justin Ehrlich & Simon Medcalfe & Shane Sanders, 2021. "Composite Index Ranking of Economic Well-Being in U.S. Metropolitan Areas: How Prevalent are Rank Anomalies?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 157(2), pages 543-562, September.
    19. Fusco, Elisa, 2023. "Potential improvements approach in composite indicators construction: The Multi-directional Benefit of the Doubt model," Socio-Economic Planning Sciences, Elsevier, vol. 85(C).
    20. Ilya Solntsev & Anatoly Vorobyev & Elnura Irmatova & Nikita Osokin, 2016. "Rating evaluation of sports development efficiency using statistical analysis: evidence from Russian football," Papers 1612.07543, arXiv.org.

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